The large capital investment required to design, test and fabricate microelectronic devices and the difficulty in redesigning and/or reworking microelectronic devices which do not operate as planned, have emphasized the need to simulate circuit performance at each stage of design and development. Accordingly, to meet this need many circuit simulators have been developed and marketed. One widely used time domain circuit simulator is a program which was developed at the Electronics Research Laboratory of the University of California, Berkeley, known as SPICE. In general, SPICE is a system for simulating nonlinear circuits in time, using nonlinear time-independent generalized admittance representations. A popular version of SPICE (SPICE 2) is described in "SPICE Version 2G.6 User's Guide" Berkeley: University of California, Department of Electrical Engineering and Computer Science, 1980 by Vladimirescu et al.
Circuit simulators have also been the subject of patent protection because they are an integral part of the design and fabrication of microelectronic devices. Recently issued patents covering circuit simulators are U.S. Pat. No. 4,918,643 to Wong entitled Method and Apparatus for Substantially Improving the Throughput of Circuit Simulators; U.S. Pat. No. 5,047,971 to Horwitz entitled Circuit Simulation; U.S. Pat. No. 5,051,911 to Kimura et al. entitled Apparatus for Effecting Simulation of a Logic Circuit and Method for Producing a Semiconductor Device Using the Simulation Approach; U.S. Pat. No. 5,313,398 to Rohrer et al. entitled Method and Apparatus for Simulating a Microelectronic Circuit; and U.S. Pat. No. 5,379,231 to Pillage et al. entitled Method and Apparatus for Simulating a Microelectronic Interconnect Circuit.
Circuit simulators are typically software based, and are designed to accept a description if the circuit which defines the circuit topology and element values. Each element in the circuit is typically specified by an element line containing the element name, the connecting nodes, and electrical parameter values. Simulators typically simulate circuits which contain passive devices such as resistors, diodes, capacitors and inductors, stimuli such as voltage and current sources and active devices such as bipolar junction transistors (BJT), junction field effect transistors (JFET) and metal oxide semiconductor field effect transistors (MOSFET). Simulators are also typically configured to perform DC analysis, AC small signal analysis and transient analysis in the time domain where the behavior of the circuit is determined as a function of time. This is in contrast to frequency domain simulation where the behavior of the circuit is determined as a function of frequency instead of time.
However, one aspect of frequency domain circuit simulation that can be particularly problematic is the simulation of circuits having nonlinear characteristics and behavior. Typical circuits exhibiting nonlinear behavior include clocked circuits such as switched-capacitor circuits. Switched-capacitor circuits have been widely used for integrating a variety of analog functions on a chip including the analog functions performed by filters, sigma-delta modulators and data converters, for example. Switched-capacitor technology has also been found suitable for analog integrated circuit design because of its ability to simulate precision resistors through ratio-matched capacitive components. Unfortunately, conventional simulators capable of generating frequency domain responses for switched-capacitor circuits using frequency domain analyses typically ignore the nonlinearities and nonidealities associated with these circuits which can be caused by charge injection, voltage dependence, the presence of finite poles and zeros and op-amp settling time, for example. Moreover, conventional nonlinear frequency domain response simulators which handle the nonlinearities using time domain analyses are typically extremely time consuming, particularly for circuits having large transient response components. Further compounding the difficulty of simulating switched-capacitor circuits is the fact that they typically include very fast switching devices which are clocked at rates much higher than the frequencies of the circuit's input signals.
Attempts have been made to address these limitations of conventional circuit simulators in simulating the frequency domain response of nonlinear circuits including switched-capacitor circuits. One attempt to simulate the behavior of switched-capacitor circuits is described in an article by K. Suyama et al. entitled Simulation of Mixed Switched-Capacitor/Digital Networks with Signal-Driven Switches, IEEE Journal of Solid-State Circuits, Vol. 25, No. 6, pp. 1403-1413, December (1990). Another attempt is described in an article by R. J. Trihy and R. A. Rohrer, entitled A Switched-Capacitor Circuit Simulator: AWEswit" IEEE Journal of Solid-State Circuits, Vol. 29, No. 3, pp. 217-225, March (1994). These attempts use charge-based formulations with idealized models for op-amps and switches to increase the speed of producing a simulation. But, because these simulators analyze a macromodel equivalent of ;the actual circuit, which is useful for obtaining a first-order approximated frequency response, they typically do not take into account many of the nonlinearities and secondary effects that may be present in the actual circuit. Some of these nonlinearites are due to the behavior of the switching devices, such as charge injection during MOS transistor switching.
To further address some of these limitations of conventional simulators, other attempts have been made which include a mixed frequency-time method (MFT), as described in an article by Kundert et al. entitled A Mixed-Frequency Time Approach for Distortion Analysis of Switching Filter Circuits, IEEE Journal of Solid-State Circuits, Vol. 24, No. 2, pp. 443-451, April (1989); and a non-linear steady-state method, as described in an article by Okumura et al. entitled An Efficient Small Signal Frequency Analysis Method of Nonlinear Circuits with Two Frequency Excitations, IEEE Transactions on Computer-Aided Design, Vol. 9, No. 3, pp. 225-235, March (1990). However, these methods are typically elaborate and use specialized formulations which may not be generally applicable to a wide range of nonlinear circuit applications. Moreover, while these latter methods may be capable of generating frequency domain responses in the presence of nonlinearities, they can be computationally expensive when the number of desired frequencies for the response is large. This is particularly true when repeated analysis of the frequency domain response of a circuit is required to provide a circuit designer with information illustrating the impact and influence of device and circuit parameter variations on overall circuit performance. Such repeated analysis is typically required to assess the manufacturability of a proposed circuit design and likely production yield. Unfortunately, repeated analysis of the circuit over a parameter range using preferred techniques such as the Monte Carlo method, is often too computationally expensive when these conventional simulators are used.
Thus, notwithstanding these attempts to simulate the performance and behavior of nonlinear microelectronic circuits, there still exists a need for simulators which are capable of generating accurate frequency domain response data for nonlinear circuits over a broad frequency range. There also exists a continuing need to develop simulators of nonlinear circuits which are highly efficient so that repeated analysis to study the effects of parametric variations can be performed efficiently and economically.